Users of regular higher-order perturbation approximations can face two problems: policy functions with odd undesirable shapes
and simulated data that explode. Kim, Kim, Schaumburg, and Sims (2008) propose an alternative, namely pruned perturbation,
which avoids the instability problem. In this paper, we document that pruned perturbation approximations have some important
drawbacks. We propose an alternative perturbation-based approximation that (i) does not have odd shapes, (ii) generates stable
time paths, and (iii) avoids the drawbacks that hamper pruning. We consider models for which the highlighted problems of regular
higher-order perturbation are relevant. We find that our alternative and pruned perturbation approximations give a good qualitative
insight in the nonlinear aspects of the true solution, but— with a few exceptions— differ from the true solution in some quantitative
aspects, especially during severe peaks and throughs.

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